Issue 40

K. Kaklis et alii, Frattura ed Integrità Strutturale, 40 (2017) 18-31; DOI: 10.3221/IGF-ESIS.40.02 19 The size effect analysis can be dated back to the 15 th century when Leonardo da Vinci stated that among cords of equal thickness, the longest is the least strong and that a cord is so much stronger … as it is shorter . That is the first statement of size effect even though the proportionality between structural size and strength was a bit exaggerated. In 1638, Galileo when founding the material strength theory rejected da Vinci’s rule, but pointed out that large animals have relatively bulkier bones than small ones. He called this statement the weakness of giants. In 1686, Mariotte conducted several experiments with ropes and deduced that a long rope and a short one always support the same weight unless a long rope happens to have a fault, whereas it will break sooner than in a shorter one. He proposed that this is a consequence of the principle of the inequality of the matter whose absolute resistance may be less in one place than another [1]. At that time, mathematics were not developed enough to properly state the statistical explanation of size effect. This was accomplished two centuries later by Weibull [2]. In rock mechanics and engineering geology, the uniaxial compression and the indirect tension test (Brazilian test) are considered to be the most widely spread methods to obtain rock strength properties and parameters such as the intact rock modulus and Poisson’s ratio. Tensile strength may be measured using the direct tension test. However, this test presents experimental difficulties and is not commonly conducted in rock mechanics laboratories. This is due to both the bending stresses and/or torsion moment caused by the eccentricity of imposed axial loads and the localized concentrated stresses caused by improper gripping of specimens [3,4]. Because of these experimental difficulties, alternative techniques have been developed to determine the tensile strength of rock. In the Brazilian test, a circular solid disc is compressed to failure across the loading diameter. Hondros [5] has analytically solved the Brazilian test configuration in the case of isotropic rocks, while Pinto [6] extended Hondros’ method to anisotropic rocks and checked the validity of his methodology on schisteous rock formation. Recent investigations have led to a closed form solution for an anisotropic disc [7,8], a series of charts for the determination of the stress concentration factors at the center of an anisotropic disc [9], and explicit representations of stresses and strains at any point of an anisotropic circular disc compressed diametrically [10]. It should be noted that the so-called “scale effect” is split up into two categories: shape and size effect. The shape effect describes the impact of the height/diameter ratio of a cylindrical specimen on rock strength properties. The size effect is defined by the influence of the absolute size (i.e., volume) of geometrically self-similar specimens. In case of cylindrical specimens this reduces the changes in diameter where the height/diameter ratio remains constant [11]. The scale effect is well known for both the compressive and tensile tests as there are numerous studies in the literature [12,13,14,15] that have investigated the effect of various factors such as size, shape, porosity, density on the uniaxial compressive strength (UCS) and the indirect tensile strength. This paper presents the effect of the size on UCS, indirect tensile strength, intact rock modulus and Poisson’s ratio for the Alfas building stone. The term “intact rock modulus” is used here instead of elastic modulus, in order to differentiate the modulus of intact rock with respect to the deformation modulus of the rock mass. T ESTING MATERIAL n order to experimentally examine the size effect on the uniaxial compressive and indirect tensile strength, specimens of Alfas building stone were tested. The Alfas stone is a micritic (microcrystalline) homogeneous limestone. X-ray diffraction (XRD) and Rietveld quantitative method [16] results, indicate that it is composed by 91% of calcite (CaCO 3 ), 2% of quartz (SiO 2 ) and 7% aragonite (CaCO 3 ). The determination of water absorption at atmospheric pressure is based on standard BS ΕΝ 13755 (2008) [17], while the determination of open (effective) porosity and bulk (apparent) density is based on standard BS EN 1936 (2006) [18]. The average results for Alfas stone are shown in Tab. 1. Water Absorption (%) Open Porosity (%) Bulk Density (kg/m 3 ) 12.19 (±0.61) 31.48 (±3.20) 2870 (±355) Table 1: Physical properties of the Alfas stone. I